Hard-sphere Model Research Articles

Numerical framework for the development of atmosphere-breathing electric propulsion for Earth and Mars atmosphere

Atmosphere-breathing electric propulsion systems provide a competitive advantage for the lower orbit altitudes since the propellant is collected directly from the atmosphere. The effectiveness of this technology depends on crucial aspects such as the collection and compression performance characterization, as well as the drag estimation and compensation. In the first part of this study, the lower Mars and Earth atmospheric characterization is derived based on current models and mission data. This characterization is a reliable dataset for the boundary conditions for the simulations carried out in the second part of this study. The proposed computational framework based on the Direct Simulation Monte Carlo method aims to investigate the collection and compression performances and to estimate the drag. The numerical comparison with a literature case validates the numerical setup presented in this study. The effect of different gas-surface interaction models is investigated by comparing the results yielded by the Maxwellian model (fully specular and partially diffuse reflection) and the Cercignani-Lampis-Lord model. Since the intermolecular collisions can become more relevant at the inlet of the ionization stage, both the variable hard and variable soft sphere models are briefly examined, as well as the inclusion of gas-phase reactions. Finally, the simulation results of the two cases for the low Mars orbit (150 and 140 km) are compared to the Earth case (180 km).

Fine‐Tuning of Elastic Properties by Modifying Ordering of Parallel Nanolayer Inclusions in Hard Sphere Crystals

It is known that changes on the microscopic, structural level of materials exert changes on their macroscopic properties, in particular elastic ones. This approach can be used to alter the elastic properties of materials. However, it is not easy to predict the impact of a particular change in the structure of crystals. The recent studies show that depending on the size, shape, and orientation of inclusions used, the resulting elastic properties may differ. Inclusions may enhance, weaken, or eliminate the auxetic properties in a hard sphere model. This study is focused on the influence of the spatial distribution of planar inclusions within the hard sphere crystal and its impact on its elastic properties. Periodic systems containing two nanolayer inclusions in the representative volume element, oriented orthogonally to ‐direction and in various spatial ordering, are considered. It has been shown that introducing layer inclusions causes the deterioration of auxetic properties in the ‐direction. However, the latter weakly depends on the spatial ordering of the inclusion layers. Moreover, changes in the size of the inclusion particles, combined with different ordering of the inclusion layers, can be used to coarsely and finely tune the elastic properties of the model crystal.

Statistical mechanics of crystal nuclei of hard spheres.

In the study of crystal nucleation via computer simulations, hard spheres are arguably the most extensively explored model system. Nonetheless, even in this simple model system, the complex thermodynamics of crystal nuclei can sometimes give rise to counterintuitive results, such as the recent observation that the pressure inside a critical nucleus is lower than that of the surrounding fluid, seemingly clashing with the strictly positive Young-Laplace pressure we would expect in liquid droplets. Here, we re-derive many of the founding equations associated with crystal nucleation and use the hard-sphere model to demonstrate how they give rise to this negative pressure difference. We exploit the fact that, in the canonical ensemble, a nucleus can be in a (meta)stable equilibrium with the fluid and measure the surface stress for both flat and curved interfaces. Additionally, we explain the effect of defects on the chemical potential inside the crystal nucleus. Finally, we present a simple, fitted thermodynamic model to capture the properties of the nucleus, including the work required to form critical nuclei.

Improvement of the properties of ionic liquids for the absorption refrigeration cycle

Ionic liquids (ILs), recognized as environmentally friendly green reagents, have good application prospects in many fields. However, their high viscosity has hindered their widespread application. Currently, an effective solution is to introduce a solvent as an additive. In this work, ethanol with different molar fractions was chosen to form working pairs with three ILs ([emim]BF4, [bmim]BF4 and [hmim]BF4), to reduce their viscosities. The densities and viscosities of the three working pairs were obtained in a temperature range of 293.15∼338.15 K, thereby determining the thermal expansion coefficients. The effects of ethanol on the volumetric and viscometric characteristics of the three ILs are discussed. To further analyze the interactions between ethanol and the ILs, excess mole volume and viscosity deviations were introduced. The interactions between different molecules were stronger than those between the same molecules in the working pairs. This is the main reason why the addition of ethanol reduces the viscosity of the three ILs. Finally, the hard-sphere model was applied to predict the viscosities of the working pairs. Upon introducing an adjustable argument, the average absolute relative deviation of the prediction for the aforementioned three ILs decreased to 4.4%, 5.9%, and 5.0%, respectively.

Comparative analysis of technological properties and microstructure of titanium powders of different classes of alloys

The results of a study of the technological properties of titanium powders of pseudo-α and pseudo-β alloys are presented. A comparative analysis of the characteristics of powder materials obtained by centrifugal spraying has been carried out. The results of the granulometric composition of the powders were obtained, and the calculation of the spatial packing of particles was applied within the framework of the hard sphere model for various fractional compositions. To compare the microstructure and mechanical properties, test samples from pseudo-α and pseudo-β titanium alloys were obtained using the hot isostatic pressing method according to selected modes.

Structural analysis of superparamagnetic colloid aggregates confined in spherical cavities under external magnetic field

In this study, we investigated the behaviour of aggregates composed of superparamagnetic colloids under the influence of an external magnetic field, confined within several spherical cavities. The study included systems of two and three cavities in contact, as well as two cavities separated by a distance d along the direction of the external field. Monte Carlo computer simulations employing a model of hard spheres with central dipoles were realised to explore the behaviour of the magnetic particles, constrained to move within pairs (and trios) of spherical cavities. The primary focus of this investigation was to elucidate the structures formed by magnetic particles within systems presented here. Chains or ribbons primarily form within the central region of the spherical cavities. The aggregates within each cavity are drawn towards one another until they make contact at the closest points of the cavities. This behaviour is replicated when there is a separation distance between the spherical cavities, including cases where three cavities are in contact. This phenomenon may explain the observed attraction between magnetoliposomes as reported in the literature [García-Jimeno et al. Nanoscale. 9 (39), 15131–15143 (2017)].

Study of the Flow Characteristics of Pumped Media in the Confined Morphology of a Ferrofluid Pump With Annular Microscale Constraints

Abstract The driving mechanism of ferrofluid micropumps under the constraints of an annular microscale morphology is not fully understood. The gap between microfabrication technology and the fundamental theory of microfluidics has become a substantial obstacle to the development and application of ferrofluid micropumps. In this study, we first theoretically analyzed the Knudsen numbers of millimeter-scale microfluids using Jacobson's molecular hard sphere model, obtaining the initial conclusion that liquid flow conforms to the continuum hypothesis in geometric morphologies with characteristic dimensions greater than 7 × 10−8 m. Subsequently, using a microscopic lens combined with the particle image velocimetry optical measurement method, the flow patterns in millimeter-scale annular flow channels were captured and we observed wall slip phenomena in which the slip length of the millimeter-scale channel approached the micron level. The slip velocity and flowrate through the cross section of the microscale channel followed a logarithmic function relationship and could be divided into rapid growth, slow growth, and stable stages. As the characteristic scale of the channel was further reduced, the linear relationship between the slip velocity and cross-sectional flowrate in the rapid growth stage was broken, and the nonlinear relationship approximated an exponential function. Finally, a theoretical model for the flow behavior of the driving fluid in a ferrofluid micropump was established using slip boundary conditions. The flow patterns in microscale ring flow under slip conditions conformed to a quadratic function.

Monte Carlo simulations of glass-forming liquids beyond Metropolis.

Monte Carlo simulations are widely employed to measure the physical properties of glass-forming liquids in thermal equilibrium. Combined with local Monte Carlo moves, the Metropolis algorithm can also be used to simulate the relaxation dynamics, thus offering an efficient alternative to molecular dynamics. Monte Carlo simulations are, however, more versatile because carefully designed Monte Carlo algorithms can more efficiently sample the rugged free energy landscape characteristic of glassy systems. After a brief overview of Monte Carlo studies of glass-formers, we define and implement a series of Monte Carlo algorithms in a three-dimensional model of polydisperse hard spheres. We show that the standard local Metropolis algorithm is the slowest and that implementing collective moves or breaking detailed balance enhances the efficiency of the Monte Carlo sampling. We use time correlation functions to provide a microscopic interpretation of these observations. Seventy years after its invention, the Monte Carlo method remains the most efficient and versatile tool to compute low-temperature properties in supercooled liquids.

Molecular interactions in ethyl caprate and 2-alcohol: Extended hard sphere framework

BackgroundThe study investigates the liquid densities and viscosities of Ethyl caprate (EC) combined with various 2-alkanols across a temperature spectrum of 293.15 to 323.15 K, aiming to understand the intermolecular interactions and deviations from ideal behavior. MethodsExperimental density and viscosity for the mixtures were measured with the SVM Stabinger viscometer. A modified rough hard-sphere theory was employed to model the viscosity of pure substances and binary liquids, incorporating temperature-dependent parameters. Significant Findings: All examined mixtures exhibited positive excess molar volumes. The modified rough hard-sphere model demonstrated a maximum viscosity error of 4.12 % for 2-hexanol in the temperature range of 293 to 323 K. For binary mixtures, the calculated values closely matched experimental data, with a maximum deviation of 3.51 % observed for the EC + 2-butanol mixture, highlighting the model's predictive accuracy.

Non-limited vibrational effect on shock-induced phase transitions of condensed fluid in hard-sphere model

The essence of fluid phase transition is the jump of physical properties distinctly induced by shock waves in the hard-sphere model. Due to the strong impact of the wave, the internal freedoms of molecules are stimulated, releasing tremendous energy that commonly triggers the phase transition. Conversely, typical thermal and dynamic jumps can be described by the Rankine–Hugoniot conditions based on the Euler equation. In the theoretical simulation, the initial density and rotational freedoms of molecules are directly regarded as the primary factors to affect processes of phase transition. However, the influence of vibrational freedom in molecules has not been discussed yet. As the increasing temperature can gradually excite the affection of vibrational freedom, it is unwise to assume that the temperature element is constant in the theory. What would be a suitable model that accurately reflects the relationship between temperature and affection from vibrational freedom? The non-limited model has been courageously attempted with the temperature range from T0 to 6T0 (T0 is unperturbed temperature). We have found that the vibrational freedom can have a great effect on properties during phase transition processes.

From Hard to Soft Dense Sphere Packings: The Cohesive Energy of Barlow Structures Using Exact Lattice Summations for a General Lennard-Jones Potential.

There are infinitely many distinguishable dense sphere packings in dimension three (Barlow structures) with maximum packing density of ρ = π/√18. While Hales [Hales, T. C. Ann. Math. 2005, 162, 1065-1185.] proved that the packing density of the most dense cubic packing cannot be surpassed, it is currently not known how the infinite possibilities of densely packed Barlow structures with different sequences of hexagonal close packed layers are energetically related compared to the well-known face centered cubic (fcc) and hexagonal close packed (hcp) structures. We demonstrate that, for a general Lennard-Jones potential, which includes the hard-sphere model as a limiting case, Barlow packings lie energetically between fcc and hcp. Exceptions to this energy sequence only occur when fcc and hcp are energetically quasi-degenerate.

Pair Potential between Poloxamer 407 Micelles in 14 wt % Aqueous Solution Clarifying the Sol-Gel-Sol Transition by Temperature Rise.

Poloxamer 407 (P407) is used as a safety-guaranteed, invaluable pharmaceutical nanocarrier. The aqueous solution of P407 exhibits sol-to-gel and gel-to-sol transitions, specifically during a temperature rise. Here, we develop a method to determine the pair potential between colloidal particles based primarily on experimental small-angle scattering data. Using this approach, the pair potential between the P407 micelles in the sol-gel-sol transition state is revealed without prelimiting any type of interaction forces. The results indicate that the increase in the attractive interaction contributes to enhancing the volume fraction, which is the decisive parameter for the gelation in terms of the Alder transition theory, i.e., the fluid-to-crystal phase transition of the hard-sphere model in the micelle system. This study demonstrates that one of the key mechanisms of the gel-to-sol transition upon heating is the enhancement of the structural fluctuation due to widening of the potential well in the intermicellar pair potential.

Surface Tension of Simple Molten Salts: Insight from a Charged Hard Sphere Model.

Surface tension of molten salts is rooted in many important phenomena in physical chemistry. We develop an analytical theory for the surface tension of molten salts, where the molten salt is described by a restricted primitive model electrolyte consisting of charged hard spheres, and surface tension is related to the formation of a cavity in the electrolyte. The integral equation theory is applied to the restricted primitive model electrolyte to derive an analytical formula of the cavity formation energy. The scaling relation of the cavity formation energy is further combined with morphological thermodynamics theory to determine the formula for surface tension. According to our formula, surface tension consists of a positive hard sphere contribution and a negative electrostatic contribution. Using the molar mass, interionic distance, density, and temperature as the input, our theory leads to a good prediction of surface tension of more than 16 molten salts at their melting point without introducing any adjustable parameters.

Effects of finite counterion size and nonhomogeneous permittivity and viscosity of the solution on the electrokinetics of a concentrated salt-free colloid.

In the present work, a general model of the electrokinetics and dielectric response of a concentrated salt-free colloid is developed which includes consideration of the finite size of the counterions released by the particles to the solution, a nonhomogeneous permittivity of the solution, the existence of Born and dielectrophoretic forces acting on the counterions, and especially the fact that the solution viscosity and diffusion counterion coefficient are allowed to be functions of the local counterion concentration. These effects have recently been discussed by J. J. López-García etal. [Phys. Rev. Fluids 4, 103702 (2019)10.1103/PhysRevFluids.4.103702] in the case of dilute colloids in general electrolyte solutions. The objective of this work is to explore the new effects and their influence on the electrokinetic response of concentrated salt-free systems. Present results confirm previous findings regarding the important increases of the dc electrophoretic mobility and dc electrical conductivity, as well as huge increments of the dynamic electrophoretic mobilities at high frequencies when finite-ion-size effects were taken into account. In addition, consideration of the viscosity of the solution and of the counterion diffusion coefficient as functions of the local counterion concentration leads to a decrease of the magnitude of the previous electrokinetic results. The theory incorporates a more convenient hard-sphere hydrodynamic model to account for the nonhomogeneous viscosity of the solution than others proposed in previous works in the literature. A comparison is elaborated on between electrokinetic and dielectric responses with different levels of complexity of the theoretical model, starting from the case of pointlike counterions and following with the inclusion in sequence of additional aspects such as finite counterion size, nonhomogeneous electrical permittivity with associated Born and dielectrophoretic effects, and, finally, position-dependent viscosity and diffusion counterion coefficient, and clearly shows the influence of individual effects on the general electrokinetic response and especially the relevant role the nonhomogeneous viscosity on the dc and ac electrokientic behavior of salt-free colloids.

General drag correlations for subsonic to supersonic flow past ordered particle arrays at low and moderate Reynolds numbers

The drag coefficient (CD) is an important and fundamental parameter for particle-fluid systems. In this study, we employed pseudo-particle modeling (PPM), which integrates a time-driven algorithm with the hard-sphere model, to investigate subsonic to supersonic flows past ordered particle arrays with three typical configurations, i.e., simple cubic (SC), body-centered cubic (BCC), and face-centered cubic (FCC), at low and moderate Reynolds numbers. The relationships between the drag coefficient and various factors including Reynolds number (Re), Mach number (Ma), solid volume fraction (εs) and array configuration were analyzed. The study found: 1) Under identical conditions, the drag coefficient varies with configurations. In most cases, CD of SC is the smallest and that of FCC is the largest. 2) At low and moderate Re (Re≤20), the CD decreases with increasing Re and Ma; when Ma≤1.0, the CD increases with increasing εs; when Ma>1.0, the variation of CD with εs differs qualitatively for the SC and BCC particle arrays. 3) For Re≤20, the CD for FCC particle arrays can be tentatively expressed as CD(Re, Ma, εs)=CD(Re) [aexp(-bMa)+(1-a)](1 + Kεsn), while the coefficients a and b are related to Re and K and n are related to Re and Ma. This study fills the absence of drag data for multi-particles in slip flow and transitional flow, thereby providing drag laws for a wide range of particle-fluid systems important for micro-chemical-engineering and aero-space technologies.

Kinetic theory of weakly ionized plasma and electrolyte mixtures including Onsager matrix and frequency dispersion effects

AbstractWe summarize the method of hydrodynamic approximation for weakly ionized plasmas developed with Klimontovich in 1962 and give a generalization to many—component systems using Onsagers matrix theory and including dispersion effects. We develop the conductivity theory of complex plasma and electrolyte mixtures based on the model of charged hard spheres with given non‐additive contact distances, including frequency‐dependent electric fields. These generalizations are made with the aim to allow applications to complex natural systems as atmospheric plasmas and seawater. Finally, we give as an example a numerical calculation of the single ion conductivities of a six‐component seawater model.

Comparative studies of role of different structure factors in various physical properties of some simple liquid metals

In the current work, the comparison of the structure factors and pair correlation functions produced by using eight different theoretical models based on the Perckus-Yevick Hard Sphere (PYHS), Hard Sphere Yukawa (HSY), Mean Spherical Approximation (MSA), Generalized Mean Spherical Approximation (GMSA), Soft Sphere (SS), One-Component Plasma (OCP), Optimized Random Phase Approximation (ORPA) and Charged Hard Sphere (CHS) models for liquid metals viz. Li, Na, K, Rb, Cs, Mg, Zn, Ca, Al, Ga, In, Pb, Sn, Bi and Sb are carried out. Our own model potential is used with the Taylor (TY) screening function in the present computation. With this, certain physical properties such as electrical transport (electrical resistivity), vibrational property (phonon dispersion), dynamical property (velocity autocorrelation function (VACF)) and static (long wavelength of structure factor) properties has also been calculated. When the several theoretical models of the structure factors of the researched simple liquid metals are compared, it is discovered that the experimental data is consistent and in good agreement with the theoretical models.

Microstructural insights on lithium aluminum silicate (LAS) glass ceramics

LAS glass-ceramics stimulate considerable attention in academic and industrial fields due to exceptional properties, such as low thermal expansion coefficient, transparency or superior mechanical strength. We report here an experimental investigation of LAS structure and microstructure using conventional techniques as XRD or S/TEM, but also an innovative technique based on electron diffraction mapping. The later gives a topography of the sample and a clear picture of the distribution between the glass and the spodumene particles. All the data converge towards a model of hard spheres where 75 % of the volume is composed of spheroid particles and 25 % of the remaining volume is composed of glass, which is present in the inter-particle interstices. These findings provide a new knowledge about the LAS system and may offer useful guidance for other researchers in ceramic community.

Exact Transport Coefficients from the Inelastic Rough Maxwell Model of a Granular Gas

Granular gases demand models capable of capturing their distinct characteristics. The widely employed inelastic hard-sphere model (IHSM) introduces complexities that are compounded when incorporating realistic features like surface roughness and rotational degrees of freedom, resulting in the more intricate inelastic rough hard-sphere model (IRHSM). This paper focuses on the inelastic rough Maxwell model (IRMM), presenting a more tractable alternative to the IRHSM and enabling exact solutions. Building on the foundation of the inelastic Maxwell model (IMM) applied to granular gases, the IRMM extends the mathematical representation to encompass surface roughness and rotational degrees of freedom. The primary objective is to provide exact expressions for the Navier–Stokes–Fourier transport coefficients within the IRMM, including the shear and bulk viscosities, the thermal and diffusive heat conductivities, and the cooling-rate transport coefficient. In contrast to earlier approximations in the IRHSM, our study unveils inherent couplings, such as shear viscosity to spin viscosity and heat conductivities to counterparts associated with a torque-vorticity vector. These exact findings provide valuable insights into refining the Sonine approximation applied to the IRHSM, contributing to a deeper understanding of the transport properties in granular gases with realistic features.

Influence of water on the properties of hydrophobic deep eutectic solvent

Deep eutectic solvent (DES) shows excellent absorption performance in the field of CO2 capture. It is considered as a new green absorption solvent to replace monoethanolamine. In the industry, the presence of water not only affects the structural stability of the solvent, but also affects its thermophysical properties. In this work, three kinds of hydrophobic DES were prepared. Based on the study of their structural characteristics and thermal stability, the density and viscosity of DES with water mixture were measured in the temperature range of 298.15 ∼ 338.15 K at atmospheric pressure. It was demonstrated that the trace water did not destroy the structure of DES, but it formed hydrogen bonds with DES. The increase water destroyed the structure of DES and formed hydrogen bonds with hydrogen bond donor (HBD) and hydrogen bond acceptor (HBA), respectively. Moreover, the hard sphere model was applied to study the viscosity, and after introducing the binary interaction parameter, the average absolute relative deviation of the mixture reduced to 4.4 ∼ 7.7 %.